The set with taper crimp has a die that seats and crimps at the same time. Without taper crimp requires one die for seating and a different die for crimping.
I think opinion is about evenly split on whether it is better to seat and crimp in one operation or two. I prefer to crimp in a separate stage. Getting the seat/crimp die set up just right is a PITA for me. For crimping I use the Lee factory crimp die. It does a very good job and setting it up is dead simple.
I use a lee factory crimp die with my hornady die set, it works great!!! Never can get the seat and crimp die to work right. When I switched over to the lee factory crimp it smoothed my loads out and everyone feeds like factory ammo. I was getting small bulges and my crimp site would not get below the max allowed. I even use it on lead which they say is a no no. But I have pulled some of the bullets after I used it and they measure the same as when I put them in. No crushing of the lead.. My 3 die set of Hornady is now a mixed 4 die set. Hornady resizer ,Lyman neck expander ( which I love) the Hornady bullet seater minus the crimp function and then the lee factory crimp die.
Works for me!!!! For my 9mm
There are two different versions of LEE Factory Crimp Dies(FCD): Rifle and Pistol.
The Rifle version uses a collet to horizontally crimp the case. With this version you can distort the bullets if you get it adjusted wrong, even jacketed bullets.
The Pistol version is nothing more than a regular crimp die (either roll crimp for revolver cartridges or taper crimp for semi-auto cartridges) but with the added feature of a case sizing ring at the base of the die. The sizing ring attempts to correct any bulges from over crimping.
Cast bullets in the Pistol version will not get crushed anymore than with the normal crimp die. But cast bullets in the Rifle version may suffer distortion from that Rifle FCD because the collet squeezes the case to form the crimp instead of rolling it over. I would probably not use the LEE FCD Rifle version on cast bullets.
The Hornady dies are excellent.
The first has a sizing die, an expander die, and a seating die. The seating die appears to have no crimp function, so you would need a taper crimp die.
The first appears the same, but has a taper crimp section in the seating die.
Since I have always separated the seating from crimping functions--even in the early '70s and a single-stage press--I would get the latter and a taper crimp die.
IF you have a Lee, Hornady, RCBS, or Dillon powder measure with a powder-through expander plug, you don't need the expander die. Thus, you might price a Hornady sizing die (this is the best sizing die, IMHO), the correct 9x19 PTE plug, the Hornady Seating die, and a Lee taper crimp die (all taper crimp dies are pretty much the same and the Lee is the least expensive).